Method and apparatus with improved estimation accuracy and robustness for fine frequency offset estimation in coherent receivers

ABSTRACT

The present disclosure provides a method and system for fine estimation of a local oscillator frequency offset of a received signal at a coherent receiver, by evaluating the probability mass function (PMF) of the signal phase of output symbols at different frequencies. At frequencies other than the actual frequency offset, the signal phase is uniformly distributed in [−π,π] such that the summation of a function of PMF values where the function is convex or concave between 0 and 1 can be utilized to determine an a frequency offset to be used by the coherent receiver.

CROSS-REFERENCE

This application is a Continuation-In-Part of U.S. patent applicationSer. No. 14/603,890 filed on Jan. 23, 2015, the entirety of which isincorporated by reference herein.

FIELD

The present disclosure relates generally to determining frequency offsetof a received signal in a data transmission system.

BACKGROUND

The delivery of data content to users, which can include for exampleInternet content, media content, and voice communications, is providedthrough a distributed data network. FIG. 1 is an example data networkdiagram showing how service provider 10 provides data content to endusers at their homes or office buildings 12, or wherever they may belocated. Depending on geographical area to be covered, variousintermediate nodes may be required to distribute the data content to theend users 12. In the example of FIG. 1, regional nodes 14 can functionas a data delivery node to users in vicinity of the regional nodes 14,and can function as a repeater for redistributing the data contentreceived from the service provider 10 to base stations 16. Base stations16 can be located in a neighborhood to facilitate delivery of datacontent to the homes or buildings 12 located nearby. The base stations16 can be configured to provide wireless services to users as well. Itshould be appreciated that the number of intermediate nodes between theservice provider 10 and the end users 12 can be adjusted depending onthe required geographical coverage of the data services.

The medium for carrying the signals representing the data contentbetween the nodes, such as between service provider 10 and the regionalnode 14, between the regional node 14 and the base stations 16, andbetween the base stations 16 and the homes or buildings 12 are datacables 18, 20 and 22. These data cables can be electrical conductingcables made of copper, or they can be optical cables which carry data inthe form of modulated laser light. It is well known that optical cableshave a much larger data bandwidth than copper cables, and have thebenefit of low signal loss over long distances. That being said, opticaldata transmission is still subject to various phenomena which candistort the optical signal, and must be compensated for in order torecover the transmitted data.

FIG. 2 is a simplified diagram of an optical data transportation link30, which includes a transmitter 32 and a coherent receiver 34 connectedto each other by an optical propagation channel 36. Each pair of nodesshown in the example data network diagram of FIG. 1 can have the opticaldata transportation link 30 presently shown in FIG. 2.

The transmitter 32 generates an optical signal comprised of twoorthogonal linear polarization components (X and Y), wherein eachcomponent is comprised of two orthogonal phase components (in-phase Iand quadrature Q) that have the same carrier frequency. The carrierfrequency is an optical wavelength supplied by a laser with phase noise.The propagation channel 36 is comprised of optical filters such ascascaded WSS, fiber, amplifiers that are the sources of chromaticdispersion (CD), nonlinear phase noise, polarization mode dispersion(PMD), polarization dependent loss (PDL), polarization dependent gain,polarization rotation and optical white Gaussian noise.

The coherent receiver 34 is comprised of an integrated coherentreceiver, photo detectors (PIN), analog to digit converters (ADC) and aDSP unit. The integrated coherent receiver 34 is the place where a localoscillator (LO), with a frequency that is closely matched to thetransmitter laser, mixes with a propagated optical signal and splits itto four signals with each being a mixture of transmitted signals. TheDSP unit is where signals are processed and data are recovered. Furtherdetails of all the above mentioned components are discussed later.

One of the problems with optical transmission is frequency wander, wherea frequency shift in the base band signal occurs relative to thefrequency at the transmitter 32. This is referred to as local oscillatorfrequency offset (LOFO), and the resulting signal at the receiver 34 hasa frequency that is not exactly matched with that of the transmitter 32.The LOFO needs to be corrected at the receiver 34 in order to recoverdata in the optical signal. In some currently known systems, the LOFOcan be as large as ±5 GHz.

Most known solutions follow a two-step approach for determining thefrequency offset of the received signal. First a coarse frequency offsetestimator (FOE) can estimate and correct LOFO to less than ±1 GHzestimation error. Then a fine estimation is executed to determine thefinal LOFO with an estimation error of less than 10 MHz. However, mostknown fine LOFO estimator solutions are very complex and thus costly toimplement, vulnerable to different types of impairments which increasethe estimation error beyond an expected threshold, or are only effectivefor specific modulation formats such as BPSK and QPSK but not for otherformats which must also be supported by the same product.

While some of the above mentioned techniques can be used, they may notbe effective for newer systems capable of increased bandwidth andincreased modulation. In other words, application of the currently knowntechniques for frequency offset estimation could result in a very slowdata recovery time at the coherent receiver 34, or worse, the coherentreceiver 34 may simply fail.

It is, therefore, desirable to provide a fine LOFO estimator system andmethod that is simple to implement, accurate in fine frequency offsetestimating, and universal such that it is compatible with all systems.

SUMMARY

It is an object of the present disclosure to obviate or mitigate atleast one disadvantage of previous fine frequency offset estimationtechniques.

In a first aspect, the present disclosure provides a method forestimating a frequency offset of a signal received at a coherentreceiver, comprising: receiving a plurality of equalized symbols;processing a probability mass function (PMF) of the plurality ofequalized symbols to provide a summation of square of PMF values at eachof the a plurality of frequencies; identifying one frequencycorresponding to a maximum value of the summation; and setting thefrequency offset of the coherent receiver to the identified frequency.

In a second aspect, the present disclosure provides a frequency offsetestimator for a coherent receiver, comprising: a probability massfunction (PMF) extractor configured to determine phases of a pluralityof equalized symbols and to determine individual probability massfunction values of the phases at each frequency within a range offrequencies; a PMF processor configured to square and sum the individualprobability mass function values to provide a summation of square of PMFvalues for each frequency; and a PMF identifier configured to identifythe maximum of the summation and a corresponding frequency, thecorresponding frequency being an estimated frequency offset for thecoherent receiver.

In a third aspect, the present disclosure provides a coherent opticaltransportation link, comprising: a transmitter for generating an opticalsignal; an optical channel configured to receive and transport theoptical signal of the transmitter; and a coherent receiver for receivingthe optical signal from the optical channel and configured to provide aplurality of equalized symbols corresponding to the optical signal, thecoherent receiver including a frequency offset estimator configured toprocess a probability mass function (PMF) of the plurality of equalizedsymbols to provide a summation of square of PMF values at each of aplurality of frequencies, and configured to identify one frequencycorresponding to a maximum value of the summation, and a carrier phaserecovery circuit configured to correct a phase of the equalized symbolsbased on the one frequency.

In a fourth aspect, the present disclosure provides a method forestimating a frequency offset of a signal received at a coherentreceiver, comprising: receiving a plurality of equalized symbols;processing a probability mass function (PMF) of the plurality ofequalized symbols to provide a summation of a function of PMF values ateach of the a plurality of frequencies where the function is one of astrictly concave function between 0 and 1, and a strictly convexfunction between 0 and 1; identifying one frequency from the pluralityof frequencies based on the summation of the function of the PMF values;and setting the frequency offset of the coherent receiver to theidentified frequency.

In a fifth aspect, the present disclosure provides a frequency offsetestimator for a coherent receiver, comprising: a probability massfunction (PMF) extractor configured to determine phases of a pluralityof equalized symbols and to determine individual probability massfunction values of the phases at each frequency within a range offrequencies; a PMF processor configured to determine a function of theindividual probability mass function values to provide a summation ofthe function of PMF values for each frequency where the function is oneof: strictly concave between 0 and 1; and strictly convex between 0 and1 and a PMF identifier configured to identify a frequency correspondingto a value of the summation, the frequency being an estimated frequencyoffset for the coherent receiver.

In a sixth aspect, the present disclosure provides a coherent opticaltransportation link, comprising: a transmitter for generating an opticalsignal; an optical channel configured to receive and transport theoptical signal of the transmitter; and a coherent receiver for receivingthe optical signal from the optical channel and configured to provide aplurality of equalized symbols corresponding to the optical signal, thecoherent receiver including a frequency offset estimator configured toprocess a probability mass function (PMF) of the plurality of equalizedsymbols to provide a summation of a function of PMF values at each of aplurality of frequencies where the function is concave or convex, andconfigured to identify one frequency from the summation between 0 and 1,and a carrier phase recovery circuit configured to correct a phase ofthe equalized symbols based on the one frequency.

Other aspects and features of the present disclosure will becomeapparent to those ordinarily skilled in the art upon review of thefollowing description of specific embodiments in conjunction with theaccompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present disclosure will now be described, by way ofexample only, with reference to the attached Figures.

FIG. 1 is a data network diagram of the prior art;

FIG. 2 is a diagram of an optical data transportation link of the priorart;

FIG. 3A is an example phase constellation diagram showing a uniformdistribution of phases of output symbols;

FIG. 3B is an example phase constellation diagram showing non-uniformdistribution of phases of output symbols;

FIG. 4A is an example plot of PMF versus K sectors at a frequency otherthan the actual frequency offset;

FIG. 4B is an example plot of PMF versus K sectors at a frequencycorresponding to the actual frequency offset;

FIG. 5 is a block diagram of an example coherent optical transportationlink according to a present embodiment;

FIG. 6 is a block diagram of example data recovery circuitry used in thesystem of FIG. 5, according to a present embodiment;

FIG. 7 is a circuit schematic of an example 2^(nd) order PLL used in thecarrier recovery circuitry of FIG. 6, according to a present embodiment;

FIG. 8 is a flow chart of a method for estimating actual frequencyoffset using a convex function p_(i) ²;

FIG. 9 is a flow chart of a method for estimating actual frequencyoffset using a convex or concave function ƒ(p);

FIG. 10 is a block diagram of the FO estimator of FIG. 6, according to apresent embodiment;

FIG. 11 is a block diagram of the PMF extractor of FIG. 9, according toa present embodiment;

FIG. 12 is a flow chart of a first method for estimating actualfrequency offset of a signal;

FIG. 13 is a flow chart of a second method for estimating actualfrequency offset of a signal, and

FIG. 14 is a plot of experimental data using the previously describedfrequency offset estimation embodiments.

DETAILED DESCRIPTION

Although the embodiments and its advantages have been described indetail, it should be understood that various changes, substitutions andalterations can be made herein without departing from the invention asdefined by the appended claims. Moreover, the scope of the presentapplication is not intended to be limited to the particular embodimentsof the process, machine, manufacture, composition of matter, means,methods and steps described in the specification. As one of ordinaryskill in the art will readily appreciate from the disclosure of thepresent invention, processes, machines, manufacture, compositions ofmatter, means, methods, or steps, presently existing or later to bedeveloped, that perform substantially the same function or achievesubstantially the same result as the corresponding embodiments describedherein may be utilized according to the present invention. Accordingly,the appended claims are intended to include within their scope suchprocesses, machines, manufacture, compositions of matter, means,methods, or steps.

The present disclosure provides a method and system for fine estimationof a local oscillator frequency offset of a received signal at acoherent receiver, by evaluating the probability mass function (PMF) ofthe signal phase of equalized symbols at different frequencies. Atfrequencies other than the actual frequency offset, the signal phase isuniformly distributed in [−π,π] such that the summation of square of PMF(PMF sum-square) values is minimized. However at the actual frequencyoffset, the signal phase is no longer uniformly distributed over [−π,π];in other words the signal phase will take some specific values in[−π,π], therefore a peak PMF sum-square value will result. This peak PMFvalue provides an indication of the actual offset frequency of thereceived signal.

The presently described embodiments utilize the PMF of the phase of theoutput symbols to determine the actual frequency offset at the coherentreceiver. It is noted that the present embodiments are described withinthe context of coherent optical receiver systems, but the embodimentsare equally applicable to wireless or other electrically wired receiversystems which employ a coherent receiver.

Prior to a detailed discussion of method and apparatus embodiments fordetermining the actual frequency offset in a coherent receiver, afurther explanation of the relationship between PMF and output signalphase follows.

FIG. 3A is an example phase constellation diagram for a set of outputsymbols at a specific frequency of evaluation. In the example of FIG.3A, the phase constellation has been divided into K=10 differentsectors, or bins, and it is assumed that the signal phases of outputsymbols at a specific frequency of the coherent receiver has beendetermined and plotted on this phase constellation diagram. Theresulting plot in the example of FIG. 3A is intended to show a uniformdistribution of the symbol phases in the range of [−π,π], and thusappears as a solid circle 40 if sufficient symbols are evaluated. Thismeans there is a substantially uniform distribution PMF for the phasesof the output symbols to be in each of the K sectors. If the PMF of thephase of the output symbols in the coherent receiver is represented byp_(i)(individual probability mass function values), then the summationof p_(i) (Σp_(i))=1, where p_(i)≧0. To minimize Σp_(i) ², using Lagrangemultipliers, one can show that the uniform distribution, i.e. all equalp_(i), minimizes Σp_(i) ². This uniform distribution of the phases ofthe output symbols corresponds to a situation where frequency offset isnot the actual frequency offset of the received signal.

Alternatively, any function ƒ(p) of the PMF values can be utilized, aslong as the function is either concave over the entire range ofprobabilities 0<=(p)=<1, or convex over the entire range ofprobabilities 0 21=p=<1. If the function is convex (e.g., ƒ(p)=p²), thesummation will have a peak at the frequency offset, as shown in FIG. 13.If the function is concave, the summation will have a notch at thefrequency offset. The mathematical definition of positive/negativeconcavity is that the derivative dƒ(p)/dp is a one-to-one function of p.Equivalently, dƒ(p)/dp is either monotonically strictly increasing ormonotonically strictly decreasing (or equivalently,

$ {{\frac{\mathbb{d}^{2}{f(p)}}{\mathbb{d}p^{2}} > 0},{\forall{{p\mspace{14mu}{or}\mspace{14mu}\frac{\mathbb{d}^{2}{f(p)}}{\mathbb{d}p^{2}}} < 0}},{\forall p}} ).$These conditions have to hold for at least the range 0<=p=<1. In thedescription below, some examples will be given using f(p)=p². A personof skill in the art will understand how to implement these examplesusing other strictly concave or strictly convex functions f(p).

In contrast, FIG. 3B is an example phase constellation diagram for a setof output symbols at the actual frequency offset. At the actualfrequency offset of the received signal, the phases of the outputsymbols will appear at M sectors out of K sectors, where M<K. In thepresent example of FIG. 3B, the phases of the output symbols will appearat K=3, K=5, K=7 and K=10, but will not appear in the remaining sectors.Accordingly, the phases are not uniformly distributed as in the exampleof FIG. 3A, and the Σp_(i) ² of FIG. 3B results in a peak value that isgreater than that of FIG. 3A. Therefore, by defining a local oscillatorfrequency offset evaluation (LOFOE) criterion as J_(DFS)(f_(DFS))=Σp_(i)² or in general Σƒ(p), where f_(DFS) is the sweep frequency, a peak inthe LOFOE criterion J_(DFS) will be observed at the sweep indexrepresenting the actual frequency offset (FO). It is noted that theLOFOE criterion J_(DFS) is a PMF based value. A sweep frequency can beone of a range of different frequencies separated by a predeterminedstep size, used to evaluate a particular J_(DFS). A sweep indexdesignates each of these distinct frequencies with an arbitrary integernumber. From this point forward, J_(DFS) is referred to as a PMFsum-square value.

FIG. 4A is an experimental plot of PMF for the different K sectors for afrequency that is not the actual frequency offset, using a limited setof output symbols. The PMF here correlates to a more uniformdistribution of the phases. FIG. 4B is an experimental plot of PMF forthe different K sectors for a frequency corresponding to the actualfrequency offset of the received signal at the coherent receiver. It isclearly shown that the PMF correlates to a non-uniform distributionindicative of a frequency at or close to the actual frequency offset. Itshould be noted that the plots of FIGS. 4A and 4B do not represent theexample phase plots of FIGS. 3A and 3B.

The value of K is set based on the desired level of phase detectionresolution. A higher K results in a larger number of smaller sectors,which will increase accuracy of the actual frequency offset estimation.Generally, as higher K is used, more memory is required as will bediscussed later. A low K value may not be useful as the resolution couldbe insufficient to distinguish between one frequency where the phasedistribution of the output symbols is distributed uniformly and anotherfrequency corresponding to the actual frequency offset where the phasedistribution of the output symbols is distributed non-uniformly.Therefore the lower limit of K for a specific coherent receiver systemcan be set as the lowest integer value before a non-uniform phasedistribution can no longer be distinguished from a uniform phasedistribution.

With the principles above in mind, embodiments for a method andapparatus for determining the actual frequency offset of a signalreceived by a coherent receiver can be developed. FIG. 5 is a blockdiagram of a coherent optical transportation link which uses the methodand apparatus according to the present embodiments. The coherent opticaltransportation link 100 includes a transmitter 102 and a coherentreceiver 104 communicatively coupled through an optical channel 106. Theoptical channel 106 includes planted fiber 108, optical filters 110 andoptical amplifiers 112. The coherent receiver 104 includes an integratedcoherent receiver 114, an analog to digital converter (ADC) 116, and adigital signal processor (DSP) unit 118. In fiber optics digitalcoherent receivers, such as coherent receiver 104, quasi-static channelimpairments and also component impairments such as chromatic dispersion(CD), state-of-polarization (SOP) rotations, polarization modedispersion (PMD), polarization-dependent loss (PDL), laser phase noise,PPM, frequency offset, I-Q and X-Y delay, I-Q imbalance, etc. arecompensated digitally in DSP unit 118. According to the presentembodiments, a frequency offset (FO) determinator that is configured toevaluate the previously mentioned PMF sum-square valueJ_(DFS)(f_(DFS))=Σp_(i) ² or in general Σƒ(p). For determining theactual frequency offset of a received signal, is implemented in the DSPunit 118 with transistor circuitry and/or predetermined circuit blockshaving specific functions.

FIG. 6 is an embodiment of a block diagram of data recovery circuitry inthe DSP unit 118 of FIG. 5. In the presently shown data recovery circuitembodiment of FIG. 6, different circuit blocks compensate individualimpairments in an efficient way to minimize the complexity of theoverall circuit. Alternately, it is possible to compensate for allimpairments in one equalizer circuit block which would require acomplicated MIMO-IIR adaptive equalizer with a large number of taps. Thedata recovery circuit 200 of FIG. 6 includes frequency domain equalizers(FDEQ) 202 and 204, a time domain equalizer such as MIMO-FIR 206, acarrier phase recovery circuit 208, a forward error correction (FEC)circuit 210, an FO estimator 212 and switches 214.

Since CD is a quasi-deterministic impairment with very long echo, CDcompensation (CDC) is done in a static frequency domain equalizer,namely by FDEQ 202 and 204. FDEQ 202 compensates for CD and matchfiltering of the horizontal polarization of the received signal, whileFDEQ 204 compensates for CD and match filtering of the verticalpolarization of the received signal. Afterwards, polarization dependentimpairments are compensated through an adaptive time-domain butterflystructure of MIMO-FIR 206. More specifically, MIMO-FIR 206 executes SOP,PDL and PMD equalization, by example. Then carrier phase recoverycircuit 208 corrects for laser line-width and phase noise of theequalized signals from MIMO-FIR 206 in each polarization. The FECcircuit 210 then executes error correction upon actual data.

The carrier phase recovery circuit 208 includes a 2^(nd) order PLL(phase locked loop) which is used for correcting the phase of thereceived signal relative to a reference frequency estimation provided bythe FO estimator 212. For reference, FIG. 7 shows a 2^(nd) order PLL ofa particular configuration which could be used in carrier phase recoverycircuit 208. In FIG. 7, φ₁ represents phase correction error, φ₂represents frequency offset correction. The PLL circuit of FIG. 7adjusts φ₂=2πf_(DFS)/f_(Baud), where f_(DFS) is provided by FO estimator212 of FIG. 6, and f_(Baud) is the baud rate of the system. In FIGS. 7,μ_(φ)and μ_(φ2) are small step size values in LMS adaptation for thephase and frequency track, respectively. Δφ is the error signal of PLLthat is the difference between the received signal phase and estimatedphase. φ₁+φ₂ is the estimated phase from PLL.

In the present embodiment, the FO estimator 212 includes PMF evaluationcircuitry for executing estimation of the actual frequency offset basedon the earlier discussed J_(DFS)(f_(DFS))=Σp_(i) ² or in general Σƒ(p)criteria for estimating the actual frequency offset of the receivedsignal. The switches 214 represent the functional turning on and off ofthe FO estimator 212. More specifically, the FO estimator 212 is usedduring initial signal acquisition of the coherent receiver, such asafter a reset event of the coherent receiver where receiving operationsare ceased. Accordingly in the example of FIG. 6, switches 214 areclosed to couple the signal output from carrier phase recovery circuit208 to FO estimator 212 after a reset event, and opened after the FOestimator 212 has provided the actual frequency offset to carrier phaserecovery circuit 208. While the FO estimator 212 is enabled, itevaluates the output of the carrier phase recovery circuit 208 atdifferent frequencies to eventually determine the actual frequencyoffset. Once determined, this actual frequency offset is stored and usedby carrier phase recovery circuit 208 to extract data. It is noted thatthe FO estimator 212 can be used with any carrier phase recovery circuitsimilar to the one shown and described in the embodiment of FIG. 6.

FIG. 8 is a flow chart which outlines the method embodiment ofestimating the actual frequency offset using the summation of thesquares of PMF values, as executed by FO estimator 212 of FIG. 6. Morespecifically, the circuits and logic of FO estimator 212 are configuredfor executing the method embodiment of FIG. 8. The method starts with areset event at 300, which can include powering up the coherent receiver.Most coherent receiver specifications provided by the manufacturerindicate a coarse frequency offset error range f_(coarse), such as 700MHz for example. Alternately, a supplemental circuit can be used toprovide a coarse estimate of the frequency offset with a similar errorrange. With this coarse frequency offset error range, a frequency sweeprange of f_(min) to f_(max) is set, where f_(min) is set as −f_(coarse)and f_(max) is set as +f_(coarse). Also, a frequency step size is setbased on the best resolution of the system. Then the method proceeds to302 where the output data of carrier phase recovery circuit 208 isiteratively sampled at all the different frequencies f, where f isstepped, or sweeped, from f_(min) to f_(max) by the step size. Morespecifically, the 2^(nd) order PLL is provided with each differentfrequency for operating on the received signal.

Following at 304, J_(DFS)(f_(DFS))= is calculated for each frequencyiteration of f_(DFS). Recall that J_(DFS) is a PMF sum-square value.This PMF value and its corresponding frequency is stored in memory. Thenproceeding to 306, the frequency having the largest J_(DFS) value isidentified. At 308, the actual frequency offset is set and provided tocarrier phase recovery circuit 208 for normal receiving operation. Thenthe FO estimator 212 can be disabled or turned off as it is no longerrequired during normal operation of the coherent receiver. Therefore,the FO estimator 212 can be seen as operating during a signalacquisition phase of operation of the coherent receiver.

FIG. 9 is a flow chart which outlines a method embodiment of estimatingthe actual frequency offset using a concave or convex function Σƒ(p), asexecuted by FO estimator 212 of FIG. 6. The method shown in FIG. 9 issimilar to FIG. 8, except that the function ƒ(p) is either concave overthe entire range of probabilities 0<=p=<1, or convex over the entirerange of probabilities 0<=p=<1. Following 302, J_(DFS) is calculated at305 where J_(DFS)(f_(DFS))=Σƒ(p) for each frequency iteration off_(DFS). This PMF value and its corresponding frequency is stored inmemory. Then proceeding to 307, a frequency associated with a J_(DFS)value is identified. The identified frequency is associated with themaximum of the summation in the case where f(p) is a convex function;and is associated with the minimum of the summation in the case wheref(p) is a concave function. At 308, the actual frequency offset is setand provided to carrier phase recovery circuit 208 for normal receivingoperation.

FIG. 10 is a block diagram showing an embodiment of the FO estimator 212of FIG. 6, according to a present embodiment. In order to simplify theschematic, block 400 is a combination of both MIMO-FIR 206 and carrierphase recovery circuit 208 of FIG. 6, and is simply referred to as theMIMO-FIR and phase recovery block 400.

The present FO estimator embodiment includes PMF extractors 402, 404,PMF processors 406, 408, a local summer 410, a global summer 412, a PMFidentifier 414, a frequency sweeper 416 and frequency offset settingcircuits 418 and 419. PMF extractor 402 and PMF processor 406 operate onone polarization of the received signal while PMF extractor 404 and PMFprocessor 408 operate on another polarization of the received signal.The group of circuit blocks 400, 402, 404, 406 and 408 can be referredto as a single PMF processing branch. Some coherent receivers may havemultiple PMF processing branches having circuit blocks identical tocircuit blocks 400, 402, 404, 406 and 408, but operating concurrently ondifferent sets of data. Such a level of parallelism can be used when asingle processor branch is not fast enough to process the stream ofinput data. Following is a discussion of PMF extractors 402, 404, PMFprocessors 406, 408, PMF identifier 414, frequency sweeper 416 andfrequency offset setting circuits 418 and 419.

During the signal acquisition phase of operation, the frequency sweeper416 is responsible for setting different f_(DFS) frequencies atpredetermined step sizes, and executes the frequency sweeping functiondiscussed at step 302 of the method embodiments of FIGS. 8 and 9. Oncef_(DFS) is set, frequency offset setting circuit 419 will set φ₂ usingthe f_(DFS) set by frequency sweeper 416. The MIMO-FIR and phaserecovery block 400 then operates using the set φ₂, and provides apolarized signal (Xe) to PMF extractor 402, where the PMF of theequalized signal phase is extracted for each frame of a data burst, atthe specific f_(DFS) frequency. This can be done for each symbol, byhaving circuits detect the phase and identifying which sectors of thephase constellation the phases are distributed (ie. as shown in FIG. 3Aand FIG. 3B). PMF extractor 402 tracks the number of times a phase isidentified in each sector out of K sectors. Table 1 below shows anexample extracted PMF of phases of symbols with K=10, where theleft-most column identifies a K identifier, the middle column lists theconstellation range for the corresponding sector, and the right-mostcolumn lists the count for identified phases of symbols in each of thephase constellation sectors.

TABLE 1 Phase Constellation Count K Sectors (p_(i)) 1 0 to π/5 5 2 π/5to 2π/5 3 3 2π/5 to 3π/5 8 4 3π/5 to 4π/5 6 5 4π/5 to π 6 6 π to 6π/5 47 6π/5 to 7π/5 3 8 7π/5 to 8π/5 5 9 8π/5 to 9π/5 4 10 9π/5 to 2π 9

As more symbols are evaluated by PMF extractor 402, the counts willincrease. Using the previous example of FIG. 3A where a uniform phasedistribution is observed, the counts in Table 1 for all the sectors willbe substantially close to each other. On the other hand, using theprevious example of FIG. 3B where a non-uniform phase distribution isobserved, the counts across all K sectors are not close. Once a specificamount of symbols have been evaluated, such as one frame of symbols, thecollected counts are then provided to PMF processor 406. PMF processor406 then executes the mathematical function of J_(DFS) _(_)_(x)(f_(DFS))=Σp_(i) ² or in general Σƒ(p) at the present offsetfrequency of f_(DFS), which corresponds to step 304 of FIG. 8 or step305 of FIG. 9 respectively. Using the example of Table 1, where J_(DFS)_(_) _(x)(f_(DFS))=Σp_(i) ²=5²+3²+8²+6² . . . +4²+9². PMF extractor 404and PMF processor 408 operate concurrently on the other polarizationwith PMF extractor 402 and PMF processor 406 in exactly the same way,except that PMF processor 408 provides J_(DFS) _(_) _(y)(f_(DFS)). BothJ_(DFS) _(_) _(x)(f_(DFS)) and J_(DFS) _(_) _(y)(f_(DFS)) are simplyadded together at local summer 410 to yield J_(DFS) _(_) _(xy)(f_(DFS))as both polarizations are facing the same frequency offset. It is notedthat PMF extractor 404 and PMF processor 408 are not required, but areincluded in the present embodiment to improve accuracy of FO estimation.

Assuming that the other PMF process branches 420 and 422 are notpresent, or not being used, the PMF processor output J_(DFS) _(_)_(xy)(f_(DFS)) is provided to PMF identifier 414. The PMF identifier 414keeps track of J_(DFS) _(_) _(xy)(f_(DFS)) value that is maximum (if aconvex function f(p) was used) or a minimum (if a concave function f(p)was used) and the corresponding f_(DFS) that resulted in it. Thisgenerally corresponds to step 306 of FIG. 8 and FIG. 9. This iterationfor one f_(DFS) is now complete, and frequency sweeper 416 changesf_(DFS) to the next frequency. This next frequency can be the previousfrequency plus a predetermined step size, and is referred to as the nextfrequency index. The previously described operations of PMF extractors402, 404 and PMF processors 406, 408 then repeats again such that a newJ_(DFS) _(_) _(xy)(f_(DFS)) is provided to PMF identifier 414.Eventually J_(DFS) _(_) _(xy)(f_(DFS)) at all frequency indices withinthe range of f_(min) to f_(max) are provided, and PMF identifier 414then sets the actual frequency offset to be the frequency where thelargest (or smallest) J_(DFS) _(_) _(xy)(f_(DFS)) value occurred. Thiscorresponds to step 308 of FIG. 8 and FIG. 9. Now the frequency offsetsetting circuit 418 is set using this actual frequency offset and thesignal acquisition phase ends so that normal receiving operations canproceed. In summary, the FO estimator of the embodiment of FIG. 10processes PMF of the equalized symbols to provide a summation of aconcave or convex function of PMF values at different frequencies, andidentifies one frequency corresponding to a maximized summation of aconcave or convex function of PMF values.

In alternate embodiments, any one or more of parallel PMF processingbranches 420 and 422 can be used to improve accuracy of the finalJ_(DFS) _(_) _(xy)(f_(DFS)) values. Since each PMF processing branch isoperating at the same f_(DFS) and φ₂ but on different sets of data, theglobal summer 412 is used to add the J_(DFS) _(_) _(xy)(f_(DFS)) valuesfrom the output of each PMF processing branch together. This globalJ_(DFS) _(—xy) (f_(DFS)) value is provided to PMF identifier 414, andthe process is repeated again for a different f_(DFS). More data allowsfor a larger difference between a J_(DFS) _(—xy) (f_(DFS)) value from auniform phase distribution and a J_(DFS) _(_) _(xy)(f_(DFS)) value froma non-uniform phase distribution corresponding to the actual frequencyoffset. It should be appreciated that such a larger difference is easierto detect. In fact, a single pairing of one PMF extractor 402 and onePMF processor 406 is sufficient for estimating the FO, and differentpairings from any combination of PMF processing branches 420 and 422 canbe concurrently active in the FO estimation embodiments.

Accordingly, further robustness can be gained by having the FO estimator212 process multiple bursts of blocks, instead of just a single burst ofblocks. In summary, the final J_(DFS) _(_) _(xy)(f_(DFS)) for allparallel PMF processing branches can be expressed with equation 1 below:

$\begin{matrix}{{{J_{DFSTOTAL}( f_{DFS} )} = {\sum\limits_{{burst} = 1}^{nBursts}\;{\sum\limits_{{processor} = 1}^{nProc}\;{\sum\limits_{j = 1}^{nPol}\;{\sum\limits_{i = 1}^{K}\;{p_{i}^{2}( f_{DFS} )}}}}}}{{J_{DFSTOTAL}( f_{DFS} )} = {\sum\limits_{{burst} = 1}^{nBursts}\;{\sum\limits_{{processor} = 1}^{nProc}\;{\sum\limits_{j = 1}^{nPol}\;{\sum\limits_{i = 1}^{K}\;{{f(p)}( f_{DFS} )}}}}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$where K is the resolution of PMF of signal phase; nPol is the number ofpolarizations that is 2 for polarization multiplexed systems and 1 forsingle polarization transmission; nProc is the number of parallel TDEQand CR processors or branches in the DSP; nBursts is number of bursts ofblocks involved in each calculation, where nBursts should be set basedon the system specifications.

FIG. 11 is a block diagram showing further details of PMF extractors 402or 404, according to a present embodiment. In this embodiment, PMFextractor 402 includes a K bin quantizer 450 and a counters block 452.The K bin quantizer 450 is responsible for detecting a phase of theinput signal and then determining which of the K sectors, or phase bins,the phase belongs in. The p(L)++ circuit 452 is a counters block, whichcan include memory or registers for keeping count of the number ofinstances a phase is detected as belonging in a particular phase bin (orK sector). Alternately, K bin quantizer 450 can be implemented as a lookup table (LUT). For example, by multiplying the detected phase φ withK/(2π(φ×K/(2π)), the resulting value can be rounded to correspond with atable having K entries. For example, if round(φ×K/(2π) )=3, then the K=3entry in the table is incremented by 1. In both embodiments, memory isrequired to store the counts.

The previously discussed embodiments of the FO estimator, such as theone shown in FIG. 10 by example, can be used in a coherent opticaltransportation link. Such a coherent optical transportation link waspreviously shown in the embodiment of FIG. 5. The presently describedcoherent optical transportation link embodiment would include thetransmitter 102, the optical channel 106 and the coherent receiver 104.The transmitter 102 generates an optical signal, which is received andtransported by the optical channel 106. The transmitter 102 can belocated at a source location such as a service provider 10, a regionalnode 14 or a base station 16 as shown in FIG. 1, and the optical channel106 can be represented by the data cables 18, 20 and 22.

The coherent receiver 104 receives the optical signal from the opticalchannel 106, and is configured to provide equalized symbolscorresponding to the optical signal using circuits such as frequencydomain equalizers (FDEQ) 202 and 204 and MIMO-FIR 206, previously shownin the embodiment of FIG. 6. The coherent receiver 104 would include afrequency offset estimator such as the frequency offset estimator 212embodiment of FIG. 6 and the embodiment of FIG. 10, and a carrier phaserecovery circuit such as the one shown by the carrier phase recoverycircuit 208 embodiment of FIG. 6. The FO estimator in the presentlydescribed coherent optical transportation link embodiment processesprobability mass function (PMF) of the equalized symbols for thepurposes of providing a summation a convex or concave function of PMFvalues at different frequencies, and identifies one frequencycorresponding to a maximized summation of square of PMF values. Thecarrier phase recovery circuit in the presently described coherentoptical transportation link embodiment corrects a phase of the equalizedsymbols based on the identified one frequency.

With reference to FIG. 12 and FIG. 13, detailed flow charts of themethods for estimating actual frequency offset of a signal in a coherentreceiver using PMF of signal phase are described. For example, thefollowing method embodiment can be executed in the circuits shown inFIGS. 5, 6 and 10. More specifically, the method embodiments of FIG. 12and FIG. 13 can be executed in the DSP 118 of the embodiment of FIG. 5,in the FO estimator 212 of the embodiment of embodiment of FIG. 6, andin the PMF extractor embodiment of FIG. 10.

The method of FIG. 12 begins at 500 after a reset event, where foFs isset to f_(min), J_(max) and J_(DFS) are set to 0, f_(est) is set tof_(min), and iBurst is set to 0. The variable f_(est) will eventually bethe actual frequency offset, f_(min) is the minimum frequency to use,J_(max) stores the greatest PMF value, and the PMF sum-square valueJ_(DFS) is a currently evaluated PMF processor output. Following at 502,φ₂ is set to 2π×f_(DFS)/f_(Baud) for the 2^(nd) order PLL of the carrierphase recovery circuit 208, and the iBurst value is incremented. Forexample, the MIMO-FIR and phase recovery block 400 is now set to operatewith the f_(DFS) and φ₂ values. As output symbols are provided fromMIMO-FIR and phase recovery block 400, the PMF of the output phase foreach symbol is determined at 504, and represented as p_(i). This iswhere counts of the phase in each of the K sectors of the phaseconstellation sectors are accumulated. Following at 506 in FIG. 12, aPMF processor calculation using a convex function such asJ_(DFS)=J_(DFS)+ΣP_(i) ² is executed for the current burst of blocks. Ifat 508 the current burst number iBurst is not greater than a maximumburst number nBurst, then the method returns to 502 to receive asubsequent burst of blocks to evaluate. As the method loops through 502,504 and 506 under the same f_(DFS) and φ₂ settings for each successiveburst of blocks, J_(DFS) continues increasing in value.

Once current burst number iBurst is greater than a maximum burst numbernBurst, then the method proceeds to 510. A comparison between thecurrent J_(DFS) and J_(max) is made at 510. Because this first iterationhas J_(max)=0 and J_(DFS) is surely >0, J_(max) is set as J_(DFS), andf_(est) is set as f_(DFS) at 516. In other words, the maximum J_(DFS) isrecorded with its corresponding frequency, and any previous lowerJ_(DFS) and corresponding frequency value is discarded or ignored. If at510 J_(DFS) is less than J_(max), then the current f_(DFS) frequency isof no interest, and the method proceeds to 512 where parameters J_(DFS)and iBurst are reset to 0, and f_(DFS) is incremented by thepredetermined frequency step size. A comparison of the newly incrementedf_(DFS) is compared to f_(max) at 514. If f_(DFS) has not exceededf_(max), then there are still more frequencies to determine PMF of theoutput phase at, so the method returns to 502 with a new f_(DFS) value.Otherwise, the method proceeds to 518 as all the frequency indices havebeen swept. By 518, the largest J_(DFS) value has been stored asJ_(max), and its corresponding frequency has been stored asf_(est),which is reported and set as the actual frequency offset for thecoherent receiver. Normal receiving operation of the coherent receivercan now proceed.

With reference to FIG. 13, the method begins at 520 after a reset event,where f_(DFS) is set to f_(min), and J_(DFS) are set to 0, f_(est) isset to f_(min), and iBurst is set to 0. The variable f_(est) willeventually be the actual frequency offset, f_(min) is the minimumfrequency to use, J_(min) stores the smallest PMF value, and the PMFfunction value J_(DFS) is a currently evaluated PMF processor output.Following at 522, φ₂ is set to 2π×f_(DFS)/f_(Baud) for the 2^(nd) orderPLL of the carrier phase recovery circuit 208, and the iBurst value isincremented. For example, the MIMO-FIR and phase recovery block 400 isnow set to operate with the f_(DFS) and φ₂ values. As output symbols areprovided from MIMO-FIR and phase recovery block 400, the PMF of theoutput phase for each symbol is determined at 524, and represented asp_(i). This is where counts of the phase in each of the K sectors of thephase constellation sectors are accumulated. Following at 526, a PMFprocessor calculation of J_(DFS)=J_(DFS)+Σƒ(p) is executed for thecurrent burst block, using a concave function f(p). If at 528 thecurrent burst number iBurst is not greater than a maximum burst numbernBurst, then the method returns to 522 to receive a subsequent burst ofblocks to evaluate. As the method loops through 522, 524 and 526 underthe same f_(DFS) and φ₂ settings for each successive burst of blocks,J_(DFS) continues increasing in value.

A comparison between the current J_(DFS) and J_(min) is made at 530.Because this first iteration has J_(min)=0 and J_(DFS) is surely>0,J_(min) is set as JDFS, and f_(est) is set as f_(DFS) at 536. In otherwords, the minimum J_(DFS) is recorded with its corresponding frequency,and any previous higher J_(DFS) and corresponding frequency value isdiscarded or ignored. If at 530 J_(DFS) is greater than J_(min), thenthe current f_(DFS) frequency is of no interest, and the method proceedsto 532 where parameters J_(DFS) and iBurst are reset to 0, and f_(DFS)is incremented by the predetermined frequency step size. A comparison ofthe newly incremented f_(DFS) is compared to f_(min) at 534. If f_(DFS)has not exceeded f_(max), then there are still more frequencies todetermine PMF of the output phase at, so the method returns to 522 witha new f_(DFS) value. Otherwise, the method proceeds to 538 as all thefrequency indices have been swept. By 538, the largest J_(DFS) value hasbeen stored as J_(min) , and its corresponding frequency has been storedas f_(est), which is reported and set as the actual frequency offset forthe coherent receiver. Normal receiving operation of the coherentreceiver can now proceed.

The previously described FO estimator embodiments have been implementedand tested to demonstrate the effectiveness of using PMF of signaloutput phase for estimating the actual frequency offset of a signalreceived by a coherent receiver. FIG. 14 is a plot of the PMF processoroutput (J_(DFS)) at different f_(DFS) frequencies whereJ_(DFS)(f_(DFS))=ΣP_(i) ². The single peak value is clearly evident inFIG. 14, and the frequency offset error is about 1 MHz, well below thetolerated maximum of 10 MHz. In similar test using prior art frequencyoffset estimation methods, the estimation error is much larger than thetolerable limits, and system fails to recover the data.

In summary, the previously described frequency offset estimation methodembodiment and system embodiment for coherent digital receiversestimates the offset frequency with higher speed, more robustness andaccuracy over currently known methods. The present embodiments using PMFof signal phase can be used with any type of signaling, such as forexample RRC, RC, NRZ and RZ67. The present embodiments using PMF ofsignal phase are compatible with all modulation schemes, including forexample BPSK, QPSK, 8QAM,16QAM and 64QAM, and with all pre-codings,pre-compensations, quantizations, and different sources of noises whichcan include amplified spontaneous emission (ASE) and phase noise byexample. The present embodiments are compatible with any DSP algorithm,insensitive to narrow electrical bandwidth, large number of WavelengthSelective Switches (WSS), larger LOFO, large ASE and large channelimpairments. The present embodiments are not complex, are hardwarefriendly, and features fast convergence as less bursts are required todetermine the offset frequency.

The previously described embodiments have been illustrated in thecontext of polarization-multiplexed coherent optical transmission,however, they can be used in single-polarization coherent opticaltransmission as well. Furthermore, the previously described embodimentscan be used in traditional wired and wireless communications systemsthat use a coherent receiver. More specifically, any coherent system caninclude the FO estimator circuits taught in the previous embodiments,and with an existing frequency corrector, can sweep the range of allpossible operating frequencies. Based on the PMF sum-square output,referred to as the PMF processor output, FO can be estimated.

In the preceding description, for purposes of explanation, numerousdetails are set forth in order to provide a thorough understanding ofthe embodiments. However, it will be apparent to one skilled in the artthat these specific details are not required. In other instances,well-known electrical structures and circuits are shown in block diagramform in order not to obscure the understanding. For example, specificdetails are not provided as to whether the embodiments described hereinare implemented as a software routine, hardware circuit, firmware, or acombination thereof.

Embodiments of the disclosure can be represented as a computer programproduct stored in a machine-readable medium (also referred to as acomputer-readable medium, a processor-readable medium, or a computerusable medium having a computer-readable program code embodied therein).The machine-readable medium can be any suitable tangible, non-transitorymedium, including magnetic, optical, or electrical storage mediumincluding a diskette, compact disk read only memory (CD-ROM), memorydevice (volatile or non-volatile), or similar storage mechanism. Themachine-readable medium can contain various sets of instructions, codesequences, configuration information, or other data, which, whenexecuted, cause a processor to perform steps in a method according to anembodiment of the disclosure. Those of ordinary skill in the art willappreciate that other instructions and operations necessary to implementthe described implementations can also be stored on the machine-readablemedium. The instructions stored on the machine-readable medium can beexecuted by a processor or other suitable processing device, and caninterface with circuitry to perform the described tasks.

The above-described embodiments are intended to be examples only.Alterations, modifications and variations can be effected to theparticular embodiments by those of skill in the art. The scope of theclaims should not be limited by the particular embodiments set forthherein, but should be construed in a manner consistent with thespecification as a whole.

What is claimed is:
 1. A method for estimating a frequency offset of asignal received at a coherent receiver, comprising: receiving aplurality of equalized symbols; processing a probability mass function(PMF) of the plurality of equalized symbols to provide a summation of afunction of PMF values at each of a plurality of frequencies where thefunction is one of a strictly concave function between 0 and 1, and astrictly convex function between 0 and 1; identifying one frequency fromthe plurality of frequencies based on the summation of the function ofthe PMF values; and setting the frequency offset of the coherentreceiver to the identified frequency.
 2. The method of claim 1, whereinthe function is a convex function, and the one frequency is identifiedby the maximum of the summation.
 3. The method of claim 1 wherein thefunction is a concave function, and the one frequency is identified bythe minimum of the summation.
 4. The method of claim 1, furthercomprising: resetting the coherent receiver before iteratively receivingthe plurality of equalized symbols in a signal acquisition phase ofoperation; and operating the coherent receiver with the frequency offsetin a normal phase of operation.
 5. The method of claim 1, whereinprocessing includes detecting phases of a frame of a data burst; andidentifying in which K sectors of a phase constellation the detectedphases are distributed, wherein K is a finite integer greater than
 1. 6.The method of claim 5, wherein processing further includes counting thedistribution of the detected phases.
 7. The method of claim 6, whereinprocessing further includes calculating a summation of the function ofthe distribution of the detected phases, the summation of the functionof the distribution of the detected phases corresponding to thesummation of the function of PMF values.
 8. The method of claim 7,wherein said identifying one frequency further includes comparing thesummation of the function of PMF values to each other to identify themaximized summation of the function of the PMF values and thecorresponding one frequency.
 9. The method of claim 1, wherein theequalized symbols include symbols from first and second polarizationcomponents of the signal.
 10. The method of claim 6, wherein processingfurther includes concurrently calculating a second summation of thefunction of the PMF values corresponding to another set of data of thesignal at the same frequency, and adding the summation of the functionof the PMF values and the second summation of the function of the PMFvalues together.
 11. A frequency offset estimator for a coherentreceiver, comprising: a probability mass function (PMF) extractorconfigured to determine phases of a plurality of equalized symbols andto determine individual probability mass function values of the phasesat each frequency within a range of frequencies; a PMF processorconfigured to determine a function of the individual probability massfunction values to provide a summation of the function of PMF values foreach frequency where the function is one of: strictly concave between 0and 1, and strictly convex between 0 and 1; and a PMF identifierconfigured to identify a frequency corresponding to a value of thesummation, the frequency being an estimated frequency offset for thecoherent receiver.
 12. The frequency offset estimator of claim 11,wherein the function is a convex function, and the frequency isidentified by a maximum of the summation.
 13. The frequency offsetestimator of claim 11, wherein the function is a concave function, andthe frequency is identified by a minimum of the summation.
 14. Thefrequency offset estimator of claim 11, wherein the PMF extractorincludes a quantizer for detecting the phases and identifying in which Ksectors of a phase constellation the detected phases are distributed,wherein K is a finite integer greater than
 1. 15. The frequency offsetestimator of claim 11, wherein the PMF extractor includes counters forcounting the distribution of the detected phases; and a memory forstoring counts of the distribution of the detected phases.
 16. Thefrequency offset estimator of claim 15, wherein the PMF extractor andthe PMF processor are a first PMF extractor and a first PMF processor,wherein the first PMF extractor receives equalized symbols correspondingto one polarization of a received optical signal and the first PMFprocessor provides a first summation of the function of PMF values. 17.The frequency offset estimator of claim 16, further comprising a secondPMF extractor and a second PMF processor, wherein the second PMFextractor receives equalized symbols corresponding to anotherpolarization of the received optical signal and the second PMF processorprovides a second summation of the function of PMF values.
 18. Thefrequency offset estimator of claim 17, further comprising a localsummer for adding the first summation of the function of PMF values tothe second summation of the function of PMF values to provide thesummation of the function of PMF values.
 19. The frequency offsetestimator of claim 17, wherein the first PMF extractor, the first PMFprocessor, the second PMF extractor and the second PMF processor areincluded in a first PMF processing branch for operating on a first setof data, and the frequency offset estimator further includes a secondPMF processing branch operating on a second set of the data concurrentlyas the first PMF processing branch, to provide a third summation of thefunction of PMF values and a fourth summation of the function of PMFvalues.
 20. The frequency offset estimator of claim 19, furthercomprising a summer for adding the first summation of the function ofPMF values, the second summation of the function of PMF values, thethird summation of the function of PMF values and the fourth summationof the function of PMF values to each other to provide the summation ofthe function of PMF values.
 21. A coherent optical transportation link,comprising: a transmitter for generating an optical signal; an opticalchannel configured to receive and transport the optical signal of thetransmitter; and a coherent receiver for receiving the optical signalfrom the optical channel and configured to provide a plurality ofequalized symbols corresponding to the optical signal, the coherentreceiver including a frequency offset estimator configured to process aprobability mass function (PMF) of the plurality of equalized symbols toprovide a summation of a function of PMF values at each of a pluralityof frequencies where the function is concave or convex, and configuredto identify one frequency from the summation between 0 and 1; and acarrier phase recovery circuit configured to correct a phase of theequalized symbols based on the one frequency.
 22. The coherent opticaltransportation link of claim 21, wherein the one frequency is identifiedby a maximum of the summation for the convex function.
 23. The coherentoptical transportation link of claim 21, wherein the one frequency isidentified by a minimum of the summation for the concave function.